WASHINGTON (CNN) -- Top Democrats have expressed concern over President Obama's plan to draw down nearly two-thirds of U.S. forces in Iraq by August 2010, while some key Republicans are offering praise.

House Speaker Nancy Pelosi earlier this week questioned the need to keep 50,000 troops in Iraq until 2011.

At issue: Obama plans to leave between 35,000 to 50,000 residual forces in the war-torn country, serving in a training or advisory role to the Iraqi military.

All U.S. troops have to be out of Iraq by December 31, 2011, under an agreement the Bush administration signed with the Iraqi government last year. There are currently 142,000 U.S. troops in Iraq.

House Speaker Nancy Pelosi, D-California, indicated earlier this week that the residual force Obama is planning to leave in Iraq is too large.

Pelosi on Wednesday told MSNBC's Rachel Maddow: "I don't know what the justification is for 50,000, a presence of 50,000 troops in Iraq. ... I do think that there's a need for some. I don't know that all of them have to be in [the] country."

"As President Obama's Iraq policy is implemented, the remaining missions given to our remaining forces must be clearly defined and narrowly focused so that the number of troops needed to perform them is as small as possible,"Pelosi said in a press release. "The president's decision means that the time has come at last for Iraq's own security forces to have the prime responsibility for Iraq's security."

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Rep. Lynn Woolsey, D-California, co-founder of the Out of Iraq House Caucus, was critical of the plan.

"I am deeply troubled by the suggestion that a force of 50,000 troops could remain in Iraq beyond this time frame," she said in a statement Friday. "Call such a troop level what you will, but such a large number can only be viewed by the Iraqi public as an enduring occupation force. This is unacceptable."

Rep. Dennis Kucinich, D-Ohio, said that while he supports Obama's "step in the right direction," the new troop plan does not "go far enough."

"You cannot leave combat troops in a foreign country to conduct combat operations and call it the end of the war. You can't be in and out at the same time," Kucinich said in a release Friday.

And top Senate Democrats echoed some of their House colleagues' skepticism.

"That's a little higher number than I expected," Majority Leader Harry Reid, D-Nevada, said Thursday.

The third-ranking Senate Democrat, Sen. Charles Schumer of New York, said, "It has to be done responsibly, we all agree. But 50,000 is more than I would have thought."

On Thursday afternoon, the president briefed bipartisan leaders from the House of Representatives and Senate -- including Sen. John McCain, R-Arizona, at the White House about the troop plan.

Sen. Carl Levin, D-Michigan, chairman of the Senate Armed Services Committee, said that 50,000 is "somewhat larger" than what he expected. However, he said he has always believed "a few tens of thousands" of troops would be needed for noncombat missions such as training and fighting terrorism. Watch Obama announce the new Iraq plan »

Before the White House meeting, Sen. Dick Durbin of Illinois, the No. 2 Senate Democrat and a close Obama ally, said he was anxious to get the troops home. But he defended the administration, saying it is "trying to strike the right balance" between ending the war and maintaining stability in Iraq.

Rep. John McHugh of New York, the top Republican on the House Armed Services Committee, said later that Obama assured him the plan to withdraw all combat forces will be revisited if conditions on the ground in Iraq deteriorate.

"The president's objective to withdraw U.S. combat troops from Iraq is one we should pray for, plan for and work toward," McHugh said in a statement.

"However, I remain concerned that the security situation in Iraq is fragile, and we should work to mitigate any risks to our troops and their mission. I specifically raised these points with the president this evening."

McHugh added, "Our commanders must have the flexibility they need in order to respond to these challenges, and President Obama assured me that there is a 'Plan B.' "

On Friday morning, McCain, who criticized Obama's plan to pull combat troops from Iraq in the presidential race, offered warm praise for the new proposal.

In a speech on the Senate floor, McCain said Obama's decision is "reasonable" and that he is "cautiously optimistic that the plan that is laid out by the president can lead to success."

McCain, the ranking Republican on the Senate Armed Services Committee, said that a "failing situation in Iraq has been arrested and reversed" due to the "dramatic success of the surge strategy," referring to President Bush's plan in 2007 to send additional troops to Iraq.

He also praised Obama's willingness to leave behind a significant residual force and reassess the situation if conditions change in the future.

"We are finally on a path to success" in Iraq, McCain said. "Let us have no crisis of confidence now."

Obama touted his opposition to the Iraq war during the presidential campaign, a position popular with liberal groups such as MoveOn.org.

But according to a new CNN/Opinion Research Corp. poll, many Democrats may not be satisfied with Obama's plan.

When asked if the U.S. should keep the same number of troops in Iraq that are currently stationed there, 12 percent of Democratic respondents agreed -- compared with 58 percent of Republican respondents. Watch more on the poll »

Asked if U.S. forces should be removed by "next spring," 87 percent of Democrats and 39 percent of Republicans surveyed were in favor.

But the survey suggested that half of all Americans think the United States is winning the war in Iraq, the highest percentage since that question was first asked in a CNN poll in 2004.

"This indicates that the public thinks the surge worked, but that hasn't changed their view of the war in Iraq at all," said Keating Holland, CNN polling director. "As a result, nearly seven out of 10 favor the idea of removing most U.S. troops from Iraq by next spring, a proposal that was a key part of Obama's presidential campaign last year."

The CNN/Opinion Research poll was conducted February 18-19, with 1,046 adult Americans questioned by telephone. The survey's sampling error is plus or minus 3 percentage points.